Introduction
In recent years spectrally efficient modulation and detection technologies have been extensively explored in the research community with the goal of further increasing the spectral efficiency and therefore the overall fiber capacity [1-8]. While fast acquisition of the carrier phase is a crucial issue in high-speed communication systems that employ large quadrature amplitude modulation (QAM) modulation schemes, the high-order M-ary quadrature amplitude modulation (QAM) such as square 16-QAM and 64-QAM have attracted great attention due to their potential to realize high speed optical transmission at high spectral efficiencies [1]-[7].
For these high-order modulation formats, however, their tolerance to the laser phase noise decreases because the Euclidean distance is decreased [8]. Carrier phase recovery algorithm with better tolerance to laser phase noise is therefore very important for successful implementation of these high-order modulation formats. Phase recovery is a crucial problem in synchronous digital communication systems, especially for high bit rate signaling such as QAM modulation. There have been many techniques to retrieve phase information in coherent receivers [4]-[16].
The phase error can be corrected applying adaptive equalization with training sequences in baseband. Recently blind equalization based on higher order statistics has attracted extensive attention. The method based on blind phase search algorithm not only employs a feed-forward configuration but also involves all the current symbols for the phase estimation, and therefore can achieve a better tolerance to phase noise [12 and 13].
In this disclosure, we proposed a novel phase estimation scheme using multiple cascaded phase recovery stages. In the first stage, eighth-order statistics (EOS) based on the signal decimation is used to improve the performance for square and cross QAM systems in the fourth-power phase estimator, at the expense of increased complexity. This means that the number of samples can be reduced by a factor of at least four [9]. The EOS based on the signal decimation blind phase recovery method employs an approximate blind phase search. In the following stages, a constellation-assisted maximum-likelihood (ML) carrier phase estimate is used to find out a more accurate phase estimate by [12 and 13].
We experimentally demonstrate that the proposed new algorithm can reduce the required computational effort by more than a factor of 3 for 16-QAM system compared to that based on the single-stage EOS method.